Single-axis simulation of state-feedback controller with bang-bang control for inchworm mobile mechanism

In this paper, we describe the design of a precise 3-axial servo controller for an inchworm mobile mechanism and the simulation result of 1-axial control for validating the design. The inchworm mobile mechanism is composed of 6 piezoelectric actuators (PAs) and a pair of electromagnets (EMs). If one EM is fixed to a ferromagnetic floor, then another EM can position the X, Y, and Θ axes by 6 PAs. In a previous study, we have developed 3-axial proportional-integral-derivative (PID) controls with a 50 nm resolution for the mechanism with 4 linear encoders to measure the 3DoF motion of the free magnet precisely, however, we concluded that we require over 100 ms of settling time because of mutual coupling effects among the X, Y, and θ axes when using the PID controller. To be robust against the disturbance and also reduce settling time, we developed a new servo controller in this study. To achieve sufficient working efficiency, we aimed at establishing of 3-axial servo control on the nanometer scale that can realize a ±0.5 μm positioning repeatability, and less than 10 ms of settling time over a 50 μm×50 μm positioning range.